Let (M, g) be a compact Riemannian n-dimensional manifold with umbilic boundary It is well know that, under certain hypothesis, in the conformal class of g there are scalar-flat metrics that have the boundary of M as a constant mean curvature hypersurface. In this paper we prove that these metrics are a compact set in the case of low dimensional manifolds, that is n = 6, 7, 8, provided that the Weyl tensor is always not vanishing on the boundary.
A compactness result for scalar-flat metrics on low dimensional manifolds with umbilic boundary
Ghimenti, Marco G.
;Micheletti, Anna Maria
2021-01-01
Abstract
Let (M, g) be a compact Riemannian n-dimensional manifold with umbilic boundary It is well know that, under certain hypothesis, in the conformal class of g there are scalar-flat metrics that have the boundary of M as a constant mean curvature hypersurface. In this paper we prove that these metrics are a compact set in the case of low dimensional manifolds, that is n = 6, 7, 8, provided that the Weyl tensor is always not vanishing on the boundary.File in questo prodotto:
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